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curve-filtering problem

DOI:
10.1111/b.9781405106795.2004.x

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P hilosophy of science A problem forst proposed by legendre (1753–1833) and Gauss (1777–1855). Curve-fitting to the data on a graph is a method of inferring from observed data. If a scientist tries to connect two variables on the grounds of a set of n data points, he will join them with a curve. There might be a family of curves that fit these n points to any desirable degree. How, then, can the scientist locate the best-fitting curve? Intuitively, and also based on common sense, a smooth curve will be chosen. But why is this one the best fitting? Philosophically, there is a problem of simplicity , that is, how we determine the simplest curve from all those curves that pass through every one of a set of data points on a graph, and how we justify choosing it. This problem is relevant not only to the definition of simplicity but also to the problem of induction . “The curve-fitting problem: two different curves are defined at all points and pass exactly through each data point, why should we think that the smooth curve is more probably true?” Sober, Simplicity ... log in or subscribe to read full text

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